Mr. J. C. Maxwell on the Dynamical Theory of Gases. 205 



Hence if the pressures as well as the temperatures be the 

 same in two gases, 



*uA (10 o) 



or the masses of the individual molecules are proportional to the 

 density of the gas. 



This result, by which the relative masses of the molecules can 

 be deduced from the relative densities of the gases, was first 

 arrived at by Gay-Lussac from chemical considerations. It is 

 here shown to be a necessary result of the Dynamical Theory of 

 Gases ; and it is so, whatever theory we adopt as to the nature 

 of the action between the individual molecules, as may be seen 

 by equation (34), which is deduced from perfectly general as- 

 sumptions as to the nature of the law of force. 



"We may therefore henceforth put - 1 for ^A where s 1} s 2 are the 



specific gravities of the gases referred to a standard gas. 



If we use 6 to denote the temperature reckoned from absolute 

 zero of a gas thermometer, M the mass of a molecule of hydro- 

 gen, V 2 its mean square of velocity at temperature unity, s the 

 specific gravity of any other gas referred to hydrogen, then the 

 mass of a molecule of the other gas is 



M = J\V; (101) 



its mean square of velocity, 



V*=-V o 2 0; (102) 



s 



pressure of the gas, 



P=if»V (103) 



We may next determine the amount of cooling by expansion. 



Cooling by Expansion. 

 Let the expansion be equal in all directions, then 



— — — — — — l ^P nm\ 



dx~ dy~~ dz~~ 3p &' ' * ' t 1U4 J 



uU 



and -j- and all terms of unsymmetrical form will be zero. 



If the mass of gas is of the same temperature throughout, 

 there will be no conduction of heat, and the equation (94) will 

 become 



iP01T-ivQ=O, .... (105) 



